Reciprocity is a fundamental property of wave propagation in linear time-invariant (LTI) media that implies invariance of a system when its inputs and outputs are exchanged and arises due to the symmetry of the medium under time-reversal. Devices that are nonreciprocal can be built by breaking the time-reversal symmetry of the medium.
Inducing nonreciprocal wave propagation is a fundamental challenge across a wide range of physical systems in electromagnetics, optics, and acoustics. Recent efforts to create nonreciprocal devices have departed from established magneto-optic methods and instead exploited momentum based techniques such as coherent spatiotemporal modulation of resonators and waveguides. However, to date the nonreciprocal frequency responses that such devices can achieve have been limited, mainly to either broadband or Lorentzian-shaped transfer functions.